Density wave mediated Dzyaloshinskii-Moriya interactions

Abstract

Anomalous transport measurements have recently been observed through a wide doping range in the cuprates. Motivated by this, we investigate the effects of a state that shares many features consistent with those of the pseudogap, the mixed triplet-singlet $d$-density wave state, and examine whether its presence could help explain these observations. For a sufficiently doped system Li and Lee (arXiv:1905.04248.) showed that that these density wave states produce a nonzero thermal Hall effect. Through the effect that density waves have on the localized spins of a square lattice in a magnetically ordered phase, we find that the mixed triplet-singlet $d$-density wave state induces stable Dzyaloshinskii-Moriya (DM) interactions among the localized spins in the presence of an external magnetic field. As similar antisymmetric exchange couplings have yielded nonzero thermal Hall contributions, we examine this induced DM interaction by applying Holstein-Primakoff (HP) transformations to study the resulting magnon excitations of the spin models for both antiferromagnetic and ferromagnetic backgrounds, relevant to the near-half-filling and heavily overdoped regimes, respectively. Furthermore, because the triplet-singlet $d$-density wave is experimentally challenging to detect directly, we discuss the magnetic signatures that this state can possibly induce away from the pseudogap regime. We calculate the magnon dispersion for ${\mathrm{La}}_{2\ensuremath{-}x}{\mathrm{Sr}}_{x}\mathrm{Cu}{\mathrm{O}}_{4}$ and find that the density wave induces a weak ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$ anisotropy; upon calculating the non-Abelian Berry curvature for this magnon branch, we show explicitly that the magnon contribution to ${\ensuremath{\kappa}}_{xy}$ is zero. Finally, we calculate corrections to the magnetic ground state energy, spin canting angles, and the spin-wave dispersion due to the topological density wave for ferromagnetic backgrounds. We find that terms linear in the HP bosons can affect the critical behavior, a point previously overlooked in the literature.